Analysis of a finite element method for Maxwell's equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations
Mathematics of Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations
SIAM Journal on Numerical Analysis
A Fast Algorithm for the Electromagnetic Scattering from a Large Cavity
SIAM Journal on Scientific Computing
An Augmented Lagrangian-Based Approach to the Oseen Problem
SIAM Journal on Scientific Computing
Block preconditioning for saddle point systems with indefinite (1, 1) block
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
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In this paper, building on the previous work by Greif and Schotzau [Preconditioners for the discretized time-harmonic Maxwell equations in mixed form, Numer. Linear Algebra Appl. 14 (2007) 281-297] and Benzi and Olshanskii [An augmented lagrangian-based approach to the Oseen problem, SIAM J. Sci. Comput. 28 (2006) 2095-2113], we present the improved preconditioning techniques for the iterative solution of the saddle point linear systems, which arise from the finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The modified block diagonal and triangular preconditioners considered are based on augmentation with using the symmetric nonsingular weighted matrix. We discuss the spectral properties of the preconditioned matrix in detail and generalize the results of the above-mentioned paper by Greif and Schotzau. Numerical experiments are given to demonstrate the efficiency of the presented preconditioners.